I do think pellets are great but they shouldn't be 100% of the diet. Nothing should make 100% of a parrot diet anyway.
I do think that people who have the smaller species of birds, like parakeets, cockatiels, lovebirds, etc should be very wary of the pellets. They have such a high number of protein in them that is way too much for the bodies of the little birds.
I also think diet will depend mainly on the species of birds. Amazon Parrots, for instance, should only have seeds as a treat because they can get obese very quick and also are likely to develop a vitamin A deficiency. Lovebirds, on the other hand, burn through more fat so they should have a few seeds in their daily diet.
I feed my Amazon parrot 40% pellets, 40% veggies, 10% fruit & 10% grains (as grains are full of carbs and that just get turned into fat). I give her sunflower seeds as a training treat only.
I feed my Lovebirds 35% pellets, 35% veggies, 10% fruit, 10% grains & 10% seeds.
But I do believe birds should be feed pellets and veggies daily and that should be the bulk of a parrots diet. (Minus Macaws who I know need a higher fat diet. Also minus the nectar diet of lorikeets, and the specialized diets of Ekkies.)
Sometimes I alternate days I feed my birds chop and pellets. One day all chop and some seeds, one day all pellets and some seeds, next day all chop, etc, etc. (Echo doesn't get any seeds, only as a treat)